Gruber, Peter M. Stability of isometries. (English) Zbl 0393.41020 Trans. Am. Math. Soc. 245, 263-277 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 81 Documents MSC: 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A45 Approximation by arbitrary linear expressions 47A65 Structure theory of linear operators 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) Keywords:Epsylon-Isometry; Stability of Isometries PDF BibTeX XML Cite \textit{P. M. Gruber}, Trans. Am. Math. Soc. 245, 263--277 (1978; Zbl 0393.41020) Full Text: DOI References: [1] P. Alexandroff and H. Hopf, Topologie. I, Springer-Verlag, Berlin-New York, 1974. Berichtigter Reprint; Die Grundlehren der mathematischen Wissenschaften, Band 45. · Zbl 0277.55001 [2] St. Banach, Théorie des opérations linéaires, Monografie Mat., PWN, Warsaw, 1932; reprint, Chelsea, New York, 1955. · JFM 58.0420.01 [3] D. G. Bourgin, Approximate isometries, Bull. Amer. Math. Soc. 52 (1946), 704 – 714. · Zbl 0060.26405 [4] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385 – 397. · Zbl 0033.37702 [5] D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223 – 237. · Zbl 0043.32902 [6] Richard D. Bourgin, Approximate isometries on finite dimensional Banach spaces, Trans. Amer. Math. Soc. 207 (1975), 309 – 328. · Zbl 0327.46023 [7] Ludwig Danzer, Detlef Laugwitz, and Hanfried Lenz, Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper einbeschriebenen Ellipsoiden, Arch. Math. (Basel) 8 (1957), 214 – 219 (German). · Zbl 0078.35803 [8] L. Danzer, B. Grünbaum and V. Klee, Helly’s theorem and its relatives, in: Convexity, Proc. Sympos. Pure Math., vol. 7, Amer. Math. Soc., Providence, R. I., 1963, pp. 101-180. · Zbl 0132.17401 [9] Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. · Zbl 0268.46013 [10] T. Figiel, On nonlinear isometric embeddings of normed linear spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 185 – 188 (English, with Loose Russian summary). · Zbl 0155.18301 [11] D. G. deFigueiredo and L. A. Karlovitz, The extension of contractions and the intersection of balls in Banach spaces, J. Functional Analysis 11 (1972), 168 – 178. · Zbl 0251.47007 [12] D. H. Hyers and S. M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288 – 292. · Zbl 0060.26404 [13] D. H. Hyers and S. M. Ulam, Approximate isometries of the space of continuous functions, Ann. of Math. (2) 48 (1947), 285 – 289. · Zbl 0029.36701 [14] Eugene Lukacs, Über die Stabilität einer Charakterisierung der Normalverteilung, Österreich. Akad. Wiss. Math.-Naturwiss. Kl. S.-B. II 185 (1976), no. 4-7, 167 – 179. · Zbl 0362.60033 [15] S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York-London, 1960. · Zbl 0086.24101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.